We have found the syllogism to be the restoration of the Notion in the judgment, and consequently the unity and truth of both. The Notion as such holds its moments sublated in unity; in the judgment this unity is internal or, what is the same thing, external; and the moments, although related, are posited as self-subsistent extremes. In the syllogism the Notion determinations are like the extremes of the judgment, and at the same time their determinate unity is posited.
Thus the syllogism is the completely posited Notion; it is therefore the rational. The understanding is regarded as the faculty of the determinate Notion which is held fast in isolation by abstraction and the form of universality. But in reason the determinate Notions are posited in their totality and unity. Therefore, not only is the syllogism rational, but everything rational is a syllogism. The syllogistic process has for a long time been ascribed to reason; yet on the other hand reason in and for itself, rational principles and laws, are spoken of in such a way that it is not clear what is the connection between the former reason which syllogises and the latter reason which is the source of laws and other eternal truths and absolute thoughts. If the former is supposed to be merely formal reason, while the latter is supposed to be creative of content, then according to this distinction it is precisely the form of reason, the syllogism, that must not be lacking in the latter. Nevertheless, to such a degree are the two commonly held apart, and not mentioned together, that it seems as though the reason of absolute thoughts was ashamed of the reason of the syllogism and as though it was only in deference to tradition that the syllogism was also adduced as an activity of reason. Yet it is obvious, as we have just remarked, that the logical reason, if it is regarded as formal reason, must essentially be recognisable also in the reason that is concerned with a content; the fact is that no content can be rational except through the rational form. In this matter we cannot look for any help in the common chatter about reason; for this refrains from stating what is to be understood by reason; this supposedly rational cognition is mostly so busy with its objects that it forgets to cognise reason itself and only distinguishes and characterises it by the objects that it possesses. If reason is supposed to be the cognition that knows about God, freedom, right and duty, the infinite, unconditioned, supersensuous, or even gives only ideas and feelings of these objects, then for one thing these latter are only negative objects, and for another thing the first question still remains, what it is in all these objects that makes them rational. It is this, that the infinitude of these objects is not the empty abstraction from the finite, not the universality that lacks content and determinateness, but the universality that is fulfilled or realised, the Notion that is determinate and possesses its determinateness in this true way, namely, that it differentiates itself within itself and is the unity of these fixed and determinate differences. It is only thus that reason rises above the finite, conditioned, sensuous, call it what you will, and in this negativity is essentially pregnant with content, for it is the unity of determinate extremes; as such, however, the rational is nothing but the syllogism.
Now the syllogism, like the judgment, is in the first instance immediate; hence its determinations are simple, abstract determinatenesses; in this form it is the syllogism of the understanding. If we stop short at this form of the syllogism, then the rationality in it, although undoubtedly present and posited, is not apparent. The essential feature of the syllogism is the unity of the extremes, the middle term which unites them, and the ground which supports them. Abstraction, in holding rigidly to the self-subsistence of the extremes, opposes this unity to them as a determinateness which likewise is fixed and self-subsistent, and in this way apprehends it rather as non-unity than as unity. The expression middle term is taken from spatial representation and contributes its share to the stopping short at the mutual externality of the terms. Now if the syllogism consists in the unity of the extremes being posited in it, and if, all the same, this unity is simply taken on the one hand as a particular on its own, and on the other hand as a merely external relation, and non-unity is made the essential relationship of the syllogism, then the reason which constitutes the syllogism contributes nothing to rationality.
First, the syllogism of existence in which the terms are thus immediately and abstractly determined, demonstrates in itself (since, like the judgment, it is their relation) that they are not in fact such abstract terms, but that each contains the relation to the other and that the middle term is not particularity as opposed to the determinations of the extremes but contains these terms posited in it.
Through this its dialectic it is converted into the syllogism of reflection, into the second syllogism. The terms of this are such that each essentially shows in, or is reflected into, the other; in other words they are posited as mediated, which they are supposed to be in accordance with the nature of the syllogism in general.
Thirdly, in that this reflecting or mediatedness of the extremes is reflected into itself, the syllogism is determined as the syllogism of necessity, in which the mediating element is the objective nature of the thing. As this syllogism determines the extremes of the Notion equally as totalities, the syllogism has attained to the correspondence of its Notion or the middle term, and its existence of the difference of its extremes; that is, it has attained to its truth and in doing so has passed out of subjectivity into objectivity.
1. The syllogism in its immediate form has for its moments the determinations of the Notion as immediate. Hence they are the abstract determinatenesses of form, which are not yet developed by mediation into concretion, but are only single determinatenesses. The first syllogism is, therefore, strictly the formal syllogism. The formalism of the syllogising process consists in stopping short at the determination of this first syllogism. The Notion, differentiated into its abstract moments, has individuality and universality for its extremes, and appears itself as the particularity standing between them. On account of their immediacy they are merely self-related determinatenesses, and one and all a single content. Particularity constitutes the middle term in the first instance since it unites immediately within itself the two moments of individuality and universality. On account of its determinateness it is on the one hand subsumed under the universal, while on the other hand the individual, as against which it possesses universality, is subsumed under it. But this concretion is in the first instance merely a duality of aspect; on account of the immediacy in which the middle term presents itself in the immediate syllogism. It appears as a simple determinateness, and the mediation which it constitutes is not yet posited. Now the dialectical movement of the syllogism of existence consists in the positing in its moments of the mediation that alone constitutes the syllogism.
is the general schema of the determinate syllogism. Individuality unites with universality through particularity; the individual is not universal immediately, but through the medium of particularity; and conversely the universal similarly is not immediately individual but descends to individuality through particularity. These determinations confront each other as extremes and are united in a different third term. Each is determinateness; in this they are identical; this their general determinateness is particularity. But they are no less extremes against this particularity than against each other, because each is present in its immediate determinateness.
The general significance of this syllogism is that the individual, which as such is infinite self-relation and therefore would be merely inward, emerges by means of particularity into existence as into universality, in which it no longer belongs merely to itself but stands in an external relationship; conversely the individual, in separating itself into its determinateness as a particularity, is in this separation a concrete individual and, as the relation of the determinateness to itself, a universal, self-related individual, and consequently is also truly an individual; in the extreme of universality it has withdrawn from externality into itself. In the first syllogism, the syllogism's objective significance is only superficially present, since in it the determinations are not yet posited as the unity which constitutes the essence of the syllogism. It is still subjective in so far as the abstract significance possessed by its terms is not thus isolated in and for itself but only in subjective consciousness. Moreover, the relationship of individuality, particularity and universality is as we have seen the necessary and essential form-relationship of the determinations of the syllogism; the defect consists not in this determinateness of the form, but in the fact that under this form each single determination is not at the same time richer. Aristotle has confined himself rather to the mere relationship of inherence, in stating the nature of the syllogism as follows: When three terms are related to one another in such a manner that one extreme is in the whole of the middle term and this middle term is in the whole of the other extreme, then these two extremes are necessarily united in a conclusion. What is expressed here is more the mere repetition of the like relationship of inherence between one extreme to the middle term, and again between the middle term and the other extreme, than the determinateness of the three terms to one another. Now since the syllogism rests on the stated relative determinateness of the terms, it is immediately evident that other relationships of the terms which are given by the other figures can only have validity as syllogisms of the understanding [Verstandesschlusse] in so far as they can be reduced to that original relationship; they are not different species of figures which stand alongside the first; on the contrary, on the one hand, in so far as they purport to be correct syllogisms, they rest solely on the essential form of the syllogism in general, which is the first figure; on the other hand, in so far as they deviate from it they are transformations into which that first abstract form necessarily passes, thereby further determining itself and advancing to totality. We shall presently see what this process is.
I-P-U is thus the general schema of the syllogism in its determinateness. The individual is subsumed under the particular, and the latter under the universal; therefore the individual too is subsumed under the universal. Or the particular inheres in the individual and the universal in the particular; therefore the universal also inheres in the individual. From one aspect, namely, in relation to the universal, the particular is subject; in relation to the individual it is predicate; or, in relation to the former it is an individual, in relation to the latter it is a universal. Because the two determinatenesses are united in it, the extremes are linked together by this their unity. The therefore appears as the conclusion that has taken place in the subject, a conclusion deduced from subjective insight into the relationship between the two immediate premises. As subjective reflection enunciates the two relations of the middle term to the extremes as particular and indeed immediate judgments or propositions, the conclusion as the mediated relation is also, of course, a particular proposition, and the consequently or therefore is the expression of the fact that it is the mediated one. But this therefore is not to be regarded as an external determination in this proposition, as if it had its ground and seat only in subjective reflection; on the contrary, it is grounded in the nature of the extremes themselves whose relation again is expressed as a mere judgment or proposition only for the purpose of, and by means of, abstractive reflection, but whose true relation is posited as the middle term. That therefore I is U is a judgment, is a merely subjective circumstance; the very meaning of the syllogism is that this is not merely a judgment, that is, not a relation effected by the mere copula or the empty is, but one effected by the determinate middle term which is pregnant with content.
Consequently, to regard the syllogism merely as consisting of three judgments, is a formal view that ignores the relationship of the terms on which hinges the sole interest of the syllogism. It is altogether a merely subjective reflection that splits the relation of the terms into separate premises and a conclusion distinct from them:
All men are mortal,
Gaius is a man,
Therefore he is mortal.
At the approach of this kind of syllogism we are at once seized with a feeling of boredom; this stems from that unprofitable form which by means of the separate propositions presents a semblance of difference that immediately dissolves in the fact itself. It is mainly this subjective shape that gives the syllogistic process the appearance of a subjective makeshift, to which reason or understanding resorts when it cannot cognise immediately. The nature of things, the rational element, certainly does not set to work by first framing for itself a major premise, the relation of a particularity to a subsistent universal, and then secondly, picking up a separate relation of an individuality to the particular, out of which thirdly and lastly a new proposition comes to light. This syllogistic process that advances by means of separate propositions is nothing but a subjective form; the nature of the fact is that the differentiated Notion determinations of the fact are united in the essential unity. This rationality is not a makeshift; on the contrary, in contrast to the immediacy of relation that still obtains in the judgment, it is the objective element; and the former immediacy of cognition is rather the merely subjective element, whereas the syllogism is the truth of the judgment. Everything is a syllogism, a Universal that through particularity is united with individuality; but it is certainly not a whole consisting of three propositions.
2. In the immediate syllogism of the understanding the terms have the form of immediate determinations; it is now to be considered from this aspect according to which they are a content. It may thus be regarded as the qualitative syllogism, just as the judgment of existence has the same aspect of qualitative determination. Accordingly the terms of this syllogism, like the terms of that judgment, are individual determinatenesses, the determinateness through its self-relation being posited as indifferent to the form and hence as content. The individual is any immediate concrete object; particularity a single one of its determinatenesses, properties or relationships; universality again a still more abstract, more individual determinateness in the particular' Since the subject as immediately determined is not yet posited in its Notion, its concretion is not reduced to the essential Notion determinations; its self-related determinateness is, therefore, an indeterminate, infinite multiplicity. In this immediacy the individual possesses an infinite number of determinatenesses which belong to its particularity, each of which therefore may constitute a middle term for it in a syllogism. But through any other middle term it is united with another universal; through each of its properties it stands in a different connection and context of existence. Further, the middle term is also a concrete in comparison with the universal; it contains several predicates itself, and the individual in turn can be united through the same middle term with several universals. In general, therefore, it is completely contingent and arbitrary which of the many properties is adopted for the purpose of connecting it with a predicate; other middle terms are transitions to other predicates, and even the same middle term may by itself be a transition to various predicates, for as a particular against the universal it contains several determinations.
But not only is an indefinite number of syllogisms equally possible for one subject and not only is any single syllogism contingent in respect of its content, but these syllogisms that concern the same subject must also pass over into contradiction. For difference in general, which in the first instance is an indifferent diversity, is no less essentially opposition. The concrete is no longer something belonging merely to the sphere of Appearance, but is concrete through the unity in the Notion of the opposites that have become determined as moments of the Notion. Now when, in accordance with the qualitative nature of the terms in the formal syllogism, the concrete is grasped in respect of a single one of the determinations belonging to it, the syllogism assigns to it the predicate corresponding to this middle term; but as from another side the opposite determinateness is inferred, this shows the former conclusion to be false, although its premises by themselves and equally its inference are quite correct. If from the middle term, that a wall has been painted blue, it is inferred that therefore the wall is blue, this is a correct inference; yet in spite of this syllogism the wall can be green if it has also been painted over yellow, from which latter circumstance taken by itself it would follow that it was yellow. If from the middle term of sense-nature it is inferred that man is neither good nor evil, because neither the one nor the other can be predicated of sense, the syllogism is correct but the conclusion is false; because as man is a concrete being, the middle term of spirituality is equally valid. From the middle term of the gravitation of the planets, satellites and comets towards the sun, it correctly follows that these bodies fall into the sun; but they do not fall into it, because each is no less its own centre of gravity, or, as it is said, they are impelled by centrifugal force. Similarly, from the middle term of sociality we can deduce the community of goods among citizens, but from the middle term of individuality, if it is pursued with equal abstractness, there follows the dissolution of the state, as has happened for example in the Holy Roman Empire from holding to the latter middle term. It is justly held that there is nothing so inadequate as a formal syllogism of this kind, since it is a matter of chance or caprice which middle term is employed. No matter how elegantly a deduction of this kind has run its course through syllogisms, however fully its correctness may be conceded it still leads to nothing of the slightest consequence, for the fact always remains that there are still other middle terms from which the exact opposite can be deduced with equal correctness. The Kantian antinomies of reason amount to nothing more than that from a notion first one of its determinations is laid down as basis, and then with equal necessity, the other. In these cases this inadequacy and contingency of a syllogism must not merely be shifted on to the content, as though these defects were independent of the form and the latter alone were the concern of logic. On the contrary, it lies in the form of the formal syllogism that the content is such a one-sided quality; it is determined to this one-sidedness by the said abstract form. It is, namely, one single quality of the many qualities or determinations of a concrete object or Notion because according to the form it is not supposed to be anything more than such an immediate, single determinateness. The extreme of individuality, as abstract individuality, is the immediate concrete, consequently the infinite or indeterminable manifold; the middle term is the equally abstract particularity, consequently a single one of these manifold qualities, and similarly the other extreme is the abstract universal. Therefore it is essentially on account of its form that the formal syllogism is wholly contingent as regards its content; and contingent, not in the sense that it is contingent for the syllogism whether this or another object be submitted to it -logic abstracts from this content- but in so far as a subject forms the basis it is contingent what kind of content determinations the syllogism shall infer from it.
3. The determinations of the syllogism are determinations of content in so far as they are immediate, abstract, and reflected into themselves. But their essential nature, on the contrary, is that they are not such mutually indifferent, intro-reflected determinations, but determinations of form; as such they are essentially relations. These relations are first, those of the extremes to the middle term-relations that are immediate, the propositiones praemissae, and, to name them, the propositio major, the relation of the particular to the universal, and the propositio minor, the relation of the individual to the particular. Secondly we have the relation of the extremes to one another, which is the mediated relation, conclusio. The immediate relations, the premises, are propositions or judgments in general, and contradict the nature of the syllogism according to which the different Notion determinations are not related immediately, but their unity should also be posited; the truth of the judgment is the syllogism. All the less can the premises remain immediate relations, since their content consists of immediately distinguished determinations and they are therefore not immediately identical in and for themselves-unless they are pure, identical propositions, that is empty tautologies that lead to nothing.
Accordingly, it is commonly demanded of the premises that they shall be proved, that is, that they likewise shall be presented as conclusions. Consequently, the two premises yield two further syllogisms. But these two new syllogisms in turn yield between them four premises which demand four new syllogisms; these have eight premises whose eight syllogisms in turn yield for their sixteen premises sixteen syllogisms, and so on in a geometrical progression to infinity.
Thus there here comes to view again the progress to infinity which appeared before in the lowlier sphere of being, but which was no longer to be expected in the domain of the Notion, of the absolute reflection-into-self out of the finite, in the region of free infinitude and truth. It was shown in the sphere of being that whenever we find the spurious infinite that runs away into a progression, we are faced with the contradiction of a qualitative being and an impotent ought-to-be that goes out and away beyond it; the progression itself is the repetition of the demand for unity in opposition to the qualitative, and of the persistent relapse into the limitation which is inadequate to that demand. Now in the formal syllogism the immediate relation or the qualitative judgment is the basis, and the mediation of the syllogism that which is posited as the higher truth over against it. The unending process of proving the premises does not resolve this contradiction but only perpetually renews it and is the repetition of one and the same original defect. The truth of the infinite progression consists, on the contrary, in the sublation of the progression itself and the form which is already determined by it as defective. This form is that of mediation as I-P-U. The two relations I-P and P-U are to be mediated relations; if this is effected in the same way the defective form I-P-U will merely be duplicated, and so on to infinity. P has to I also the form determination of a universal, and to U the form determination of an individual, because these relations are, in general, judgments. Therefore they require mediation; but mediation in the form just mentioned only results in the re-appearance of the relationship that was to have been sublated.
The mediation must therefore be effected in another manner. For the mediation of P-U, we have I; accordingly the mediation must take the form P-I-U. To mediate I-P, we have U; this mediation therefore becomes the syllogism I-U-P.
When we examine this transition in the light of its Notion, we find in the first place that the mediation of the formal syllogism is, as has been shown, contingent in respect of its content. The immediate individual has in its determinatenesses an indeterminable number of middle terms, and these in turn have a similar number of determinatenesses in general; so that it depends entirely on an external caprice or simply on some external circumstance and contingent determination, with what kind of a universal the subject of the syllogism shall be united. As regards content, therefore, the mediation is not anything necessary or universal; it is not grounded in the Notion of the fact; on the contrary, the ground of the syllogism is something external to it, that is, something immediate; but among the Notion-determinations the immediate is the individual.
As regards the form, the mediation likewise has for its presupposition the immediacy of the relation; therefore the mediation is itself mediated, and mediated by the immediate, that is, the individual. More precisely, through the conclusion of the first syllogism, the individual has become the mediating factor. The conclusion is I-U; the individual is thereby posited as a universal. In one premise, the minor I-P, it is already present as a particular; hence it is that in which these two determinations are united. Or we may say that the conclusion in and for itself enunciates the individual as a universal, and that too not in an immediate manner but through mediation; consequently as a necessary relation. The simple particularity was the middle term; in the conclusion this particularity is posited in its developed form as the relation of the individual and universality. But the universal is still a qualitative determinateness, a predicate of the individual; the individual in being determined as a universal is posited as the universality of the extremes or as the middle term; by itself it is the extreme of individuality, but because it is now determined as a universal it is at the same time the unity of the two extremes.
1. The truth of the first qualitative syllogism is that something is united with a qualitative determinateness as a universal, not in and for itself but through a contingency or in an individuality. In such a quality, the subject of the syllogism has not returned into its Notion, but is apprehended only in its externality; immediacy constitutes the ground of the relation and consequently the mediation; thus the individual is in truth the middle term.
But further, the syllogistic relation is the sublation of the immediacy; the conclusion is not an immediate relation but relation by means of a third term; it contains therefore a negative unity; consequently the mediation is now determined as possessing within itself a negative moment.
In this second syllogism the premises are: P-I and I-U; only the first of these premises is still immediate; the second, I-U, is already mediated, namely by the first syllogism. The second syllogism therefore presupposes the first, just as conversely the first presupposes the second. Here the two extremes are distinguished as particular and universal; thus the latter still keeps its place; it is predicate. But the particular has changed places; it is subject, or posited in the determination of the extreme of individuality, just as the individual is posited in the determination of middle term, or of particularity. Both are therefore no longer the abstract immediacies that they were in the first syllogism. However, they are not yet posited as concretes; in standing in the place of the other, each is posited in its own determination and at the same time, though only externally, in the determination of the other.
The specific and objective meaning of this syllogism is that the universal is not in and for itself a determinate particular — for on the contrary it is the totality of its particulars — but is one such of its species through the medium of individuality; the rest of its species are excluded from it by the immediate externality. On the other hand the particular likewise is not immediately and in and for itself the universal, but the negative unity strips it of its determinateness and thereby raises it into universality. The individuality stands in a negative relationship to the particular in so far as it is supposed to be its predicate; it is not predicate of the particular.
2. But in the first instance the terms are still immediate determinatenesses; they have not of themselves developed into any objective significance; the altered position which two of them occupy is the form, which is as yet only external to them. Therefore they are still, as in the first syllogism, simply a mutually indifferent content-two qualities that are connected, not in and for themselves, but by means of a contingent individuality.
The syllogism of the first figure was the immediate syllogism or, otherwise expressed, the syllogism in its Notion as abstract form which has not yet realised itself in its determinations. The transition of this pure form into another figure is on the one hand the beginning of the realisation of the Notion, in that the negative moment of mediation, and thereby a further determinateness of form, is posited in the initially immediate qualitative determinateness of the terms. But this is at the same time an alteration of the pure form of the syllogism; the latter no longer completely corresponds to its pure form, and the determinateness posited in its terms differs from the original form determination. Regarded merely as a subjective syllogism proceeding in an external reflection, it counts as a species of syllogism which ought to correspond to the genus, namely to the general schema I-P-U. But to begin with it does not correspond to this; its two premises are P-I, or I-P, and I-U; hence the middle term is in both cases subsumed or in both cases the subject, in which accordingly the two other terms inhere. It is therefore not a middle term, for this should on the one hand subsume or be predicate, and on the other hand be subsumed or be subject, or one of the terms should inhere in it while it itself inheres in the other. The true meaning of the fact that this syllogism does not correspond to the general form of the syllogism, is that the general form has passed over into this syllogism since the truth of that form consists in its being a subjective and contingent connecting of the terms. If the conclusion in the second figure (that is, without taking advantage of the restriction about to be mentioned, which converts it into something indeterminate) is correct, then it is so because it is so on its own account, not because it is the conclusion of this syllogism. But the same is the case with the conclusion of the first figure; it is this, its truth, that is posited by the second figure. In the view that holds the second figure to be merely one species, the necessary transition of the first into this second form is overlooked and the former is adhered to as the true form. Consequently, if in the second figure (which from ancient custom is quoted without further reasons as the third) we are likewise supposed to have a syllogism correct in this subjective sense, then it would have to be conformable to the first; hence, since one premise I-U has the relationship of the subsumption of the middle term under one extreme, then it would have to be possible to give the other premise, P-I, the opposite relation to that which it has and to subsume P under I. But such a relation would be the sublation of the determinate judgment I is P, and could only occur in an indeterminate, in a particular judgment; consequently the conclusion in this figure can only be particular. The particular judgment, however, as remarked above, is both positive and negative — a conclusion to which for that very reason no great value can be attached. Since too the particular and universal are the extremes, and are immediate, mutually indifferent determinatenesses, their relationship is itself indifferent; either can be taken at choice as major or minor term and therefore, too, either premise can be taken as major or minor.
3. The conclusion, being positive as well as negative, is thus a relation indifferent to these determinatenesses and hence a universal relation. More precisely, the mediation of the first syllogism was in itself a contingent one; in the second syllogism this contingency is posited. Hence it is the self-sublating mediation; the mediation has the determination of individuality and immediacy; what is united by this syllogism must on the contrary be in itself and immediately identical; for this middle term, immediate individuality, is determined in an infinitely manifold and external manner. In it, therefore, is rather posited the self-external mediation. But the externality of the individuality is universality; the above mediation by means of the immediate individual points beyond itself to its other form, and the mediation is therefore effected by the universal. In other words, what is to be united by the second syllogism must be conjoined immediately; the immediacy on which this syllogism is based cannot bring about a definite conclusion. The immediacy to which it points is the opposite to its own-the sublated first immediacy of being-therefore the universal that is reflected into itself, or the implicit, abstract universal.
From the point of view we have just considered, the transition of this syllogism was an alteration like transition in the sphere of being, because the qualitative element, that of immediate individuality, lies at its base. But according to the Notion, individuality unites the particular and universal in so far as it sublates the determinateness of the particular, and this presents itself as the contingency of this syllogism; the extremes are not united by their determinate relation which they have for a middle term; this term is therefore not their determinate unity, and the positive unity which still attaches to the middle term is only abstract universality. But with the positing of the middle term in this determination, which is its truth, we have another form of the syllogism.
1. This third syllogism no longer has any immediate premise; the relation I-U has been mediated by the first syllogism, the relation P-U by the second. Hence it presupposes the first two syllogisms; but conversely, they both presuppose it, and in general each presupposes the other two. In this figure, therefore, the determination of the syllogism is in general completed. What this reciprocal mediation precisely contains is this, that each syllogism, although by itself mediation, is none the less not in its own self the totality of the mediation but contains an immediacy whose mediation lies outside it.
The syllogism I-U-P, regarded in itself, is the truth of the formal syllogism; it expresses that the mediation of the formal syllogism is the abstractly universal mediation, and that the extremes are not contained in the middle term according to their essential determinateness but only according to their universality; and that therefore what was supposed to be mediated in it is precisely what is not brought into unity. Here then is made explicit in what the formalism of the syllogism consists; its terms have an immediate content which is indifferent to the form, or, what is the same thing, they are determinations of form which have not yet reflected themselves into determinations of content.
2. The middle term of this syllogism is indeed the unity of the extremes, but a unity in which abstraction is made from their determinateness; it is the indeterminate universal. But since this universal is at the same time distinguished as abstract from the extremes as determinate, it is itself still a determinate relatively to them, and the whole is a syllogism whose relation to its Notion has now to be considered. The middle term, as the universal, is the subsuming term or predicate to both its extremes, and does not occur once as subsumed or as subject. In so far, therefore, as it is supposed to correspond, as a species of syllogism, to the syllogism, it can do so only on condition that when one relation I-U, already possesses the proper relationship, the other relation U-P also possesses it. This occurs in a judgment in which the relationship of subject and predicate is indifferent, in a negative judgment. In this way the syllogism becomes legitimate, but the conclusion necessarily negative.
Thus it is now also indifferent which of the two determinations of this proposition is taken as predicate and which as subject; and in the syllogism, whether it is taken as extreme of individuality or of particularity, therefore as minor or major term. Since on the common assumption it depends on this which of the premises is to be major and which minor, this too has become a matter of indifference. This is the ground of the ordinary fourth figure of the syllogism, a figure unknown to Aristotle and which in any case is concerned with a wholly empty and pointless distinction. In it the immediate position of the terms is the reverse of their position in the first figure. Since subject and predicate of the negative conclusion in the formal treatment of the judgment do not have the definite relationship of subject and predicate, but either can take the place of the other, it is indifferent which term is taken as subject and which as predicate; therefore equally indifferent which premise is taken as major and which as minor. This indifference, aided as it is by the determination of particularity (especially when it is observed that this can be taken in the comprehensive sense) makes this fourth figure a sheer futility.
3. The objective significance of the syllogism in which the universal is the middle term, is that the mediating element, as unity of the extremes, is essentially a universal. But since the universality is in the first instance only qualitative or abstract universality, it does not contain the determinateness of the extremes; their conjunction, if it is to be effected, must similarly have its ground in a mediation lying outside this syllogism and is in respect of this latter just as contingent as in the case of the preceding forms of the syllogism. But now since the universal is determined as the middle term, and the determinateness of the extremes is not contained in it, this middle term is posited as a wholly indifferent and external one.
As the immediate result of this bare abstraction, we obtain, of course, a fourth figure of the syllogism, namely that of the relationless syllogism U-U-U, which abstracts from the qualitative difference of the terms and consequently has for its determination their merely external unity, namely their equality.
1. The mathematical syllogism runs: if two things or determinations are equal to a third, they are equal to each other. Here the relationship of inherence or subsumption of the terms is extinguished.
The mediating factor is a third in general, but it has absolutely no determination whatever as against its extremes. Each of the three can therefore equally well be the third, mediating term. Which one is to be used for this purpose, and which of the three relations, therefore, are to be taken as immediate and which as mediated, depends on external circumstances and other conditions, namely on which two of them are the immediately given terms. But this determination does not concern the syllogism itself and is completely external.
2. The mathematical syllogism ranks as an axiom in mathematics, as an absolutely self-evident, primitive proposition, that neither admits nor requires any proof, that is any mediation, and neither presupposes anything else nor can be deduced from anything else. If its prerogative of being immediately self-evident is looked at more closely, it will be seen that it lies in the formalism of this syllogism which abstracts from all qualitative distinction of the terms and only takes up their quantitative equality or inequality. But for this very reason it is not without presupposition or unmediated; the quantitative determination, which is the only thing in it taken into account, is only through abstraction from qualitative difference and from the determinations of the Notion. Lines, figures, posited as equal to one another, are understood only in terms of their magnitude; a triangle is affirmed to be equal to a square, but not as triangle to square, but only in regard to magnitude, etc. Similarly, the Notion and its determinations do not enter into this syllogising; there is no comprehending at all [that is, in terms of the Notion] in this process; and understanding too has not even the formal, abstract determinations of the Notion before it. The self-evidence of this syllogism, therefore, rests merely on the fact that its thought content is so meagre and abstract.
3. But the result of the syllogism of existence is not merely this abstraction from all Notional determinateness; the negativity of the immediate, abstract determinations which emerged from it has yet another positive side, namely that the abstract determinateness has had its other posited in it and thereby has become concrete.
In the first place, the syllogisms of existence all mutually presuppose one another and the extremes united in the conclusion are only genuinely and in and for themselves united in so far as they are otherwise united by an identity that has its ground elsewhere; the middle term, as it is constituted in the syllogisms we have considered, is supposed to be their Notion unity, but is only a formal determinateness that is not posited as their concrete unity. But this presupposed element of each of those mediations is not merely a given immediacy in general, as in the mathematical syllogism, but is itself a mediation, namely, for each of the two other syllogisms. Therefore what we truly have before us is not mediation based on a given immediacy, but mediation based on mediation. Hence this is not the quantitative mediation that abstracts from the form of mediation, but rather the mediation that relates itself to mediation, or the mediation of reflection. The circle of reciprocal presupposing that these syllogisms unite to form with one another is the return of this act of presupposition into itself, which herein forms a totality, and thus the other to which each individual syllogism points is not placed through abstraction outside the circle but embraced within it.
Further, from the side of the individual determinations of the form it has been seen that in this entirety of the formal syllogisms each individual term has in turn taken the place of middle term. This was determined as particularity; subsequently, through the dialectical movement it determined itself as individuality and universality. Similarly, each of these determinations occupied in turn the places of the two extremes. The merely negative result is the extinction of the qualitative form determinations in the merely quantitative, mathematical syllogism. But what we truly have here is the positive result, that mediation is not effected through an individual qualitative determinateness of form, but through the concrete identity of the determinations. The defect and formalism of the three syllogistic figures considered above consists just in this, that an individual determinateness of this kind was supposed to constitute their middle term. Mediation has thus determined itself as the indifference of the immediate or abstract form determinations and as positive reflection of one into the other. The immediate syllogism of existence has thereby passed over into the syllogism of reflection.
In the account here given of the nature of the syllogism and its various forms, passing reference has also been made to what in the usual consideration and treatment of syllogisms constitutes the main interest, namely, how a correct conclusion may be obtained in each figure; however, in those references only the main point has been indicated, and those cases and complexities which arise when the distinction of positive and negative judgments, together with the quantitative determination — especially particularity — is also dragged in, have been passed over. Some remarks on the ordinary view and mode of treatment of the syllogism in logic will be in place here. It is a familiar fact that this doctrine was elaborated into such finely drawn distinctions that its so-called subtleties have been the object of universal aversion and disgust. The natural understanding in asserting itself in every department of mental and spiritual culture against the unsubstantial forms of reflection, also turned against this artificial knowledge of the form of reason and supposed itself able to dispense with such a science on the ground that it performed the individual operations of thought specified therein naturally and spontaneously without any special instruction. In point of fact, if a precondition of rational thinking were the laborious study of syllogistic formulae, mankind would in that respect be in the same sorry plight as they would be, as already remarked in the Preface in another respect, if they could not walk or digest without having studied anatomy and physiology. Granting that the study of these sciences may not be without profit for the regulation of one's diet, we must undoubtedly credit the study of the forms of reason with an even more important influence on the correctness of thinking. But without going into this aspect of the matter which concerns the education of subjective thinking and therefore, strictly speaking, pedagogics, it must be admitted that the study which has for its subject matter the modes and laws of operation of reason, must in its own self be of the greatest interest-of an interest at least not inferior to an acquaintance with the laws of nature and of her particular forms. If it is not thought a small matter to have discovered some sixty species of parrots, one hundred and thirty-seven species of veronica, etc., much less ought it to be thought a small matter to discover the forms of reason; is not a figure of the syllogism something infinitely superior to a species of parrot or veronica?
Therefore, though contempt for the knowledge of the forms of reason must be regarded as sheer barbarism, equally we must admit that the ordinary presentation of the syllogism and its particular formations is not a rational cognition, not an exposition of them as forms of reason, and that syllogistic wisdom by its own worthlessness has brought upon itself the contempt which has been its lot. Its defect consists in its simply stopping short at the understanding's form of the syllogism in which the Notion determinations are taken as abstract, formal terms. It is all the more inconsequent to cling to these determinations as abstract qualities, since in the syllogism it is their relations that constitute the essential feature, and inherence and subsumption already imply that the individual, because the universal inheres in it, is itself a universal, and the universal, because it subsumes the individual, is itself an individual; more exactly, the syllogism expressly posits this very unity as middle term, and its determination is precisely mediation, that is, the Notion determinations no longer, as in the judgment, have for basis their mutual externality, but rather their unity. It is thus the Notion of the syllogism that declares the imperfection of the formal syllogism in which the middle term is fixedly held, not as unity of the extremes but as a formal, abstract determination qualitatively distinct from them. The treatment is rendered still less meaningful by the fact that also relations or judgments in which even formal determinations become indifferent, as in negative and particular judgments, and which therefore approximate to propositions, are still regarded as perfect relationships. Now since the qualitative form I-P- U is generally accepted as the ultimate and absolute, the dialectical treatment of the syllogism no longer operates; the remaining syllogisms are consequently regarded not as necessary alterations of that first form but as species. In this case, it is indifferent whether the first formal syllogism itself is regarded only as a kind of species alongside the rest, or as genus and species at the same time; the latter occurs when the other syllogisms are reduced to the first. If this reduction is not expressly effected, yet the basis is always the same formal relationship of external subsumption expressed by the first figure. This formal syllogism is the contradiction that the middle term which is supposed to be the determinate unity of the extremes does not appear as this unity but as a determination qualitatively distinct from those extremes whose unity it is supposed to be. Because the syllogism is this contradiction, it is in its own nature dialectical. Its dialectical movement exhibits it in each of the moments of the Notion, so that not only the above relationship of subsumption or particularity, but equally essentially negative unity and universality are moments in the union of the extremes. In so far as each of these by itself is equally only a one-sided moment of particularity, they are likewise imperfect middle terms, but at the same time they constitute the developed determinations of the middle term; the entire course through the three figures presents the middle term in each of these determinations, and the true result that emerges from it is that the middle is not an individual Notion determination but the totality of them all.
The defect of the formal syllogism, therefore, does not lie in the form of the syllogism — on the contrary, this is the form of rationality — but in the fact that the form appears only as an abstract and therefore notionless form. It has been shown that the abstract determination, on account of its abstract relation-to-self, can equally be regarded as content; this being so, the formal syllogism merely serves to show that a relation of a subject to a predicate follows or does not follow only from this middle term. Nothing is gained in having proved a proposition by a syllogism of this kind; on account of the abstract determinateness of the middle term, which is a Notionless quality, other middle terms can just as well be given from which the opposite follows; in fact, from the same middle term opposite predicates may in turn be deduced by further syllogisms. Besides being of little service, the formal syllogism is also a very simple affair; the numerous rules which have been invented are tiresome not only because they contrast so strongly with the simple nature of the fact but also because they relate to cases where the formal worth of the syllogism is furthermore diminished by the external form determination, above all, particularity (especially as for this purpose it must be taken in a comprehensive sense), and where even in respect of form nothing but completely worthless results are deduced. However, the most merited and most important aspect of the disfavour into which syllogistic doctrine has fallen is that this doctrine is such a long-drawn out, notionless occupation with a subject matter whose sole content is the Notion itself. The numerous syllogistic rules remind one of the procedure of arithmeticians who similarly give a host of rules about arithmetical operations, all of which rules presuppose that one has not the Notion of the operation. But numbers are a notionless material and the operations of arithmetic are an external combining or separating of them, a mechanical procedure-indeed, calculating machines have been invented which perform these operations; whereas it is the harshest and most glaring of contradictions when the form determinations of the syllogism, which are Notions, are treated as a notionless material.
The extreme example of this irrational treatment of the Notion determinations of the syllogism is surely Leibniz's subjection of the syllogism to the calculus of combinations and permutations and has reckoned thereby how many positions of the syllogism are possible — that is, with respect to the distinctions of positive and negative, of universal, particular indeterminate and singular judgments; 2,048 such combinations are found to be possible of which, after the exclusion of the useless figures, twenty-four useful figures remain. Leibniz makes much of the usefulness of the analysis of combinations for ascertaining not only the forms of the syllogism but also the combinations of other concepts. The operation by which this is ascertained is the same as that by which it is calculated how many combinations of letters are possible in an alphabet, how many throws are possible in a game of dice, how many kinds of play with an ombre card, etc. Here therefore we find the determinations of the syllogism put in the same class with the points of the die and the ombre card, the rational is taken as a dead and non-rational thing, and the characteristic feature of the Notion and its determinations as spiritual essences to relate themselves and through this relating to sublate their immediate determination, is ignored. This Leibnizian application of the calculus of combinations and permutations to the syllogism and to the combination of other notions, differed from the notorious Art of Lully solely in being more methodical on the arithmetical side, but for the rest, they were both equally meaningless. Connected with this was a pet idea of Leibniz, embraced by him in his youth, and in spite of its immaturity and shallowness not relinquished by him even in later life, the idea of a characteristica universalis of notions-a language of symbols in which each notion would be represented as a relation proceeding from others or in its relation to others as though in rational combinations, which is essentially dialectical, a content still retained the same determinations that it possesses when fixed in isolation.
Ploucquet's calculus has undoubtedly got hold of the most consistent method by which the relationship of the syllogism is made capable of being subjected to a calculus. It rests upon the abstraction from the difference of relationship, from the difference of individuality, particularity and universality in the judgment and upon strict adherence to the abstract identity of subject and predicate whereby they are in a mathematical equality — in a relation which converts the syllogising process into a completely meaningless and tautological formulation of propositions. In the proposition: the rose is red, the predicate is not to denote red in general but only the specific red of the rose; in the proposition: all Christians are men, the predicate is to denote only those men who are Christians; from this proposition and the proposition: the Jews are not Christians, there follows the conclusion (which did not particularly commend this syllogistic calculus to Mendelssohn) therefore the Jews are not men (namely, not those men that the Christians are). Ploucquet states as a consequence of his discovery: 'posse etiam rudes mechanics totam logicam doceri, uti pueri arithmeticam docentur, ita quidem, ut nulla formidine in ratiociniis suis errands torqueri, vel fallaciis circumveniri possint, si in calculo non errant.' This recommendation, that by means of the calculus the whole of logic can be mechanically brought within reach of the uneducated, is surely the worst thing that can be said of a discovery bearing on the presentation of the science of logic.
B. The Syllogism of Reflection
The course of the qualitative syllogism has sublated what was abstract in its terms with the result that the term has posited itself as a determinateness in which the other determinateness is also reflected. Besides the abstract terms, the syllogism also contains their relation, and in the conclusion this relation is posited as mediated and necessary; therefore each determinateness is in truth posited not as an individual, separate one, but as a relation to the other, as a concrete determinateness.
The middle term was abstract particularity, by itself a simple determinateness, and was a middle term only externally and relatively to the self-subsistent extremes. Now it is posited as the totality of the terms; as such it is the posited unity of the extremes, but in the first instance it is the unity of reflection which embraces them within itself — an inclusion which, as the first sublating of immediacy and the first relating of the terms, is not yet the absolute identity of the Notion.
The extremes are the determinations of the judgment of reflection, individuality proper and universality as a connective determination or a reflection embracing a manifold within itself. But the individual subject also contains, as we have seen in the case of the judgment of reflection, besides the bare individuality which belongs to form, determinateness as universality absolutely reflected into itself, as presupposed, that is here still immediately assumed, genus.
From this determinateness of the extremes which belongs to the progressive determination of the judgment, there results the precise content of the middle term, which is essentially the point of interest in the syllogism since it distinguishes syllogism from judgment. It contains (1) individuality, but (2) individuality extended to universality as all, (3) universality which forms the basis and absolutely unites within itself individuality and abstract universality — that is, the genus. It is in this way that the syllogism of reflection is the first to possess genuine determinateness of form, in that the middle term is posited as the totality of the terms; the immediate syllogism is by contrast indeterminate, because the middle term is still only abstract particularity in which the moments of its Notion are not yet posited. This first syllogism of reflection may be called the syllogism of allness.
1. The syllogism of allness is the syllogism of understanding in its perfection, but is as yet no more than that. That the middle term in it is not abstract particularity but is developed into its moments and is therefore concrete, is indeed an essential requirement for the Notion; but the form of allness so far only gathers the individual externally into universality, and conversely still preserves the individual in the universality as something possessing immediately a separate self-subsistence. The negation of the immediacy of the determinations which was the result of the syllogism of existence, is only the first negation, not yet the negation of the negation or absolute reflection into self. Therefore the single determinations still form the basis of the universality of reflection that embraces them within itself; in other words, allness is still not the universality of the Notion but the external universality of reflection.
The syllogism of existence was contingent because its middle term, as a single determinateness of the concrete subject, admits of an indeterminable number of other such middle terms, and therefore the subject could be united in the syllogism within determinably different and even contradictory predicates. But since the middle term now contains individuality and is thereby itself concrete, it can only serve to connect the subject with a predicate which belongs to the subject as concrete. If for example from the middle term green it should be inferred that a picture was pleasing because green is pleasing to the eye, or that a poem or building was beautiful because it possessed regularity, the picture, etc., might all the same be ugly on account of other qualities from which this latter predicate could be inferred. On the other hand, since the middle term has the determination of allness, it contains the greenness or regularity as a concrete, which just for that reason is not the abstraction of something merely green or merely regular; with this concrete then only those predicates can be connected which conform to the totality of the concrete thing. In the judgment: what is green or regular is pleasing, the subject is only the abstraction of green or regularity; in the proposition: all green or regular things are pleasing, the subject is, on the contrary: all actual concrete objects that are green or regular —objects, therefore, which are taken as concrete with all their properties that they possess besides greenness or regularity.
2. But this very perfection of the syllogism of reflection makes it a mere delusion. The middle term has the determinateness 'all'; to this is immediately attached in the major premise the predicate that is united with the subject in the conclusion. But 'all' are 'all individuals'; therefore in the major premise the individual subject already immediately possesses this predicate and does not obtain it first through the syllogism. Or to put it otherwise the subject obtains through the conclusion a predicate as a consequence; but the major premise already contains this conclusion within it; therefore the major premise is not correct on its own account, or is not an immediate, presupposed judgment, but already presupposes the conclusion whose ground it was supposed to be. In the favourite perfect syllogism:
All men are mortal
Now Gaius is a man
Therefore Gaius is mortal,
the major premise is correct only because and in so far as the conclusion is correct; if Gaius should chance to be not mortal, the major premise would not be correct. The proposition which was supposed to be the conclusion must already be immediately correct on its own account, because otherwise the major premise could not embrace all individuals; before the major premise can pass as correct, there is the prior question whether the conclusion itself may not be an instance against it.
3. In the case of the syllogism of existence we found from the Notion of the syllogism that the premises, as immediate, contradicted the conclusion, that is to say the mediation demanded by the Notion of the syllogism, and that the first syllogism therefore presupposed others and conversely these others presupposed it. In the syllogism of reflection, this is posited in the syllogism itself, namely, that the major premise presupposes its conclusion, in that the former contains that connection of the individual with a predicate which is supposed to appear only as conclusion.
What, then, we really have here may be expressed in the first instance by saying that the syllogism of reflection is only an external, empty show of syllogising — hence that the essence of this syllogising rests on subjective individuality and that therefore this latter constitutes the middle term and is to be posited as such the individuality that is individuality as such and possesses universality only externally. We may also say that the precise content of the syllogism of reflection showed that the relation in which the individual stands to its predicate is immediate, not inferred, and that the major premise, the connection of a particular with a universal, or, more precisely, of a formal universal with an intrinsic universal, is mediated by the relation of individuality which is present in the former — of individuality as allness. But this is the syllogism of induction.
1. The syllogism of allness comes under the schema of the first figure, I-P-U; the syllogism of induction under that of the second, U-1-P, as it again has individuality for middle term, not abstract individuality but individuality as complete, namely, posited with its opposite determination, universality. One extreme is some predicate or other that is common to all these individuals; its relation to them constitutes the immediate premises, of which one, in the preceding syllogism was supposed to be the conclusion. The other extreme may be the immediate genus as it is found in the middle term of the preceding syllogism or in the subject of the universal judgment and which is exhausted in all the individuals or species collectively of the middle term. Accordingly the syllogism has the shape:
i
i
U- -P
i
i
ad
infinitum
2. The second figure of the formal syllogism U-I-P did not correspond to the schema, because I which constitutes the middle term was not the subsuming term or predicate. In induction this defect is eliminated; here the middle term is all the individuals; the proposition: U-I, which contains as subject the objective universal or genus separated off to form an extreme, has a predicate that is at least coextensive with the subject, and consequently for external reflection is identical with it. Lion, elephant, and so on constitute the genus of quadruped; the difference, that the same content is posited once in individuality and again in universality, is accordingly a mere indifferent determination of form-an indifference which is the result of the formal syllogism posited in the syllogism of reflection, and here is posited through the equality of extension.
Induction, therefore, is not the syllogism of mere perception or of contingent existence, like the corresponding second figure, but the syllogism of experience — of the subjective taking together of the individuals into the genus and of the conjoining of the genus with a universal determinateness because this latter is found in all the individuals. It has also the objective significance that the immediate genus determines itself through the totality of individuality to a universal property, has its existence in a universal relationship or mark. But the objective significance of this, as of the other syllogisms, is at first only its inner Notion, and is not yet posited here.
3. On the contrary, induction is still essentially a subjective syllogism. The middle terms are the individuals in their immediacy; the subjective taking together of them into the genus by means of allness is an external reflection. On account of the persistent immediacy of the individuals and their consequent externality, the universality is only completeness, or rather remains a problem. In induction, therefore, the progress into the spurious infinite once more makes its appearance; individuality is supposed to be posited as identical with universality, but since the individuals are no less posited as immediate, that unity remains only a perennial ought-to-be; it is a unity of likeness; those which are supposed to be identical are, at the same time, supposed not to be so. It is only when the a, b, c, d, e are carried on to infinity that they constitute the genus and give the completed experience. The conclusion of induction thus remains problematical.
But induction, in expressing that perception in order to become experience ought to be carried on to infinity, presupposes that the genus [Kind] is in and for itself united with its determinateness. Therefore, strictly speaking, it rather presupposes its conclusion as something immediate, just as the syllogism of allness presupposes the conclusion for one of its premises. An experience that rests on induction is accepted as valid although the perception is admittedly incomplete; but the assumption that no contradictory instance of that experience can arise is only possible if the experience is true in and for itself. Thus the syllogism by induction, though indeed based on an immediacy, is not based on that immediacy on which it is supposed to be based, on the merely affirmative immediacy of individuality, but on the immediacy which is in and for itself, the universal immediacy. The fundamental character of induction is that it is a syllogism; if individuality is taken as the essential, but universality as only the external, determination of the middle term, then the middle term would fall asunder into two unconnected parts and we should not have a syllogism; this externality belongs rather to the extremes. It is only as immediately identical with universality that individuality can be the middle term; such universality is properly objective universality, the genus [Kind]. This may also be looked at in this way: universality is external but essential in the determination of individuality that forms the basis of the middle term of induction; but such an external is no less immediately its opposite, the internal. The truth of the syllogism of induction is, therefore, a syllogism that has for its middle term an individuality that is immediately in its own self universality; this is the syllogism of analogy.
1. This syllogism has for its abstract schema the third figure of the immediate syllogism I-U-P. But its middle term is no longer just any single quality, but universality that is the reflection-into-self of a concrete, and hence its nature; and conversely, because it is thus the universality of a concrete, it is at the same time in its own self this concrete. Here, then, the middle term is an individual but an individual taken in its universal nature; further, another individual forms an extreme possessing the same universal nature with the former. For example:
The earth is inhabited,
The moon is an earth,
Therefore the moon is inhabited.
2. Analogy is the more superficial, the more the universal in which the two individuals are one, and according to which one individual becomes the predicate of the other, is a mere quality, or (quality being taken subjectively) some mark or other, when the identity of the two therein is taken as a mere similarity. Superficiality of this kind, however, to which a form of understanding or reason is reduced by being degraded to the sphere of mere representation, should not find a place in logic at all. Also it is improper to represent the major premise of this syllogism as though it should run: that which resembles an object in some characteristics resembles it in others also. By so doing, the form of the syllogism is expressed in the shape of a content, while the empirical content, the content properly so called, is relegated to the minor premise. In this way the whole form, for example, of the first syllogism, could be expressed as its major premise: That which is subsumed under some other thing in which a third inheres, has also that third inherent in it: now .... and so forth. But the importance of the syllogism itself does not depend on the empirical content, and to convert its own form into the content of a major premise is no less a matter of indifference than to take any other empirical content for that purpose. But in so far as the importance of the syllogism of analogy does not depend on the former content which contains nothing but the form peculiar to the syllogism, then the importance of the first syllogism would not depend on it either, that is to say, would not depend on that which makes the syllogism a syllogism. The main point always is the form of the syllogism, whether it have the form itself or something else for its empirical content. Thus the syllogism of analogy is a peculiar form, and it is quite futile not to regard it as such on the ground that its form can be converted into the content or matter of a major premise, whereas logic is not concerned with the matter. What may lead to this misunderstanding in the case of the syllogism of analogy and perhaps also in the case of the syllogism of induction, is that in them the middle term and the extremes, too, are further determined than in the merely formal syllogism, and therefore the form determination, because it is no longer simple and abstract, must appear also as a determination of content. But the fact that the form determines itself to content in this way is in the first place a necessary advance of the formal element and therefore essentially concerns the nature of the syllogism; and therefore, secondly, a content determination of this kind cannot be regarded in the same way as any other empirical content, nor can abstraction be made from it.
When we consider the form of the syllogism of analogy in the above expression of its major premise, which states that if two objects agree in one or more properties, then a property which one possesses also belongs to the other, it may seem that this syllogism contains four terms, the quaternio terminorum — a circumstance which entails the difficulty of bringing analogy into the form of a formal syllogism. There are two individuals, thirdly, a property immediately assumed as common, and fourthly the other property which one individual immediately possesses but which the other first obtains through the syllogism. This arises from the fact that, as we have seen, in the analogical syllogism the middle term is posited as individuality, but immediately also as the true universality of the latter. In induction, the middle term is, apart from the two extremes, an indeterminable number of individuals; in this syllogism therefore an infinite number of terms ought to be enumerated. In the syllogism of allness the universality in the middle term is so far merely the external form determination of allness; in the syllogism of analogy, on the contrary, it is essential universality. In the above example the middle term, the earth, is taken as a concrete that in its truth is as much a universal nature or genus as an individual.
From this aspect, the quaternio terminorum would not render analogy an imperfect syllogism. Yet it does so from another aspect; for although one subject has the same universal nature as the other, it is undetermined whether the determinateness which is inferred for the second subject belongs to the first by virtue of its nature or by virtue of its particularity; whether for example the earth is inhabited as a heavenly body in general, or only as this particular heavenly body. Analogy is still a syllogism of reflection inasmuch as individuality and universality are immediately united in its middle term. On account of this immediacy, the externality of the unity of reflection is still with us; the individual is only implicitly the genus, it is not posited in that negativity by which its determinateness would be the determinateness proper to the genus itself. For this reason the predicate which belongs to the individual of the middle term is not already predicate of the other individual although both belong to the one genus.
3. I-P (the moon is inhabited) is the conclusion; but one premise (the earth is inhabited) is likewise I-P; inasmuch as I-P is supposed to be a conclusion it involves the demand that the said premise shall be one also. Hence this syllogism is in its own self the demand for itself to counter the immediacy which it contains, in other words it presupposes its conclusion. A syllogism of existence has its presupposition in the other syllogisms of existence; in the case of the syllogisms just considered the presupposition has been placed within them, because they are syllogisms of reflection. Since then the syllogism of analogy is the demand for its own mediation against the immediacy with which its mediation is burdened, it is the moment of individuality whose sublation it demands. Thus there remains for middle term the objective universal, the genus, purged of immediacy. In the syllogism of analogy the genus was a moment of the middle term only as an immediate presupposition; since the syllogism itself demands the sublation of the presupposed immediacy, the negation of the individuality, and consequently the universal, is no longer immediate, but posited. The syllogism of reflection contained only the first negation of immediacy; now the second has appeared, and with it the external universality of reflection is determined into universality in and for itself. Regarded from the positive side the conclusion shows itself to be identical with the premise, the mediation as having coincided with its presupposition; thus there is an identity of the universality of reflection by which it has become a higher universality.
Looking over the course of the syllogisms of reflection, we see that the mediation is in general the posited or concrete unity of the form determinations of the extremes; the reflection consists in this positing of one determination in the other; thus the mediating element is allness. But individuality appears as the essential ground of allness and universality only as an external determination in it, as completeness. But universality is essential to the individual if it is to be a middle term that unites; the individual is therefore to be taken as in itself a universal. But the individual is not united with universality in this merely positive manner but is sublated in it and a negative moment; thus the universal is that whose essential being has become actual, the posited genus, and the individual as immediate is rather the externality of the genus, or it is an extreme. The syllogism of reflection taken in general comes under the schema P-I-U, in which the individual is still as such the essential determination of the middle term; but in that its immediacy has sublated itself, and the middle term has determined itself as the universality that is in and for itself, the syllogism has entered under the formal schema I-U-P, and the syllogism of reflection has passed over into the syllogism of necessity.
The mediating element has now determined itself (1) as simple determinate universality, like the particularity in the syllogism of existence, but (2) as objective universality, that is to say, universality which contains the entire determinateness of the distinguished extremes like the allness of the syllogism of reflection, a fulfilled yet simple universality-the universal nature of the fact, the genus.
This syllogism is pregnant with content, because the abstract middle term of the syllogism of existence posited itself as determinate difference to become the middle term of the syllogism of reflection, while this difference has reflected itself into simple identity again. This syllogism is therefore the syllogism of necessity, for its middle term is not some alien immediate content, but the reflection-into-self of the determinateness of the extremes. These possess in the middle term their inner identity, the determinations of whose content are the form determinations of the extremes. Consequently, that which differentiates the terms appears as an external and unessential form, and the terms themselves as moments of a necessary existence.
In the first instance this syllogism is immediate, and thus formal in so far as the connection of the terms is the essential nature as content, and this content is present in the distinguished terms in only a diverse form, and the extremes by themselves are merely an unessential subsistence. The realisation of this syllogism has so to determine it that the extremes also shall be posited as this totality which initially the middle term is, and that the necessity of the relation which is at first only the substantial content, shall be a relation of the posited form.
1. The categorical syllogism has the categorical judgment for one or both of its premises. Here, with this syllogism, as with the judgment, is associated the more specific significance that its middle term is objective universality. Superficially the categorical syllogism too is taken for nothing more than a mere syllogism of inherence.
The categorical syllogism in its substantial significance is the first syllogism of necessity, in which a subject is united with a predicate through its substance. But substance raised into the sphere of the Notion is the universal, posited as being in and for itself in such a manner that it has for the form or mode of its being, not accidentality, which is the relationship peculiar to substance, but the Notion-determination. Its differences are therefore the extremes of the syllogism and, precisely, universality and individuality. The former, in contrast to the genus, which is the precise determination of the middle term, is abstract universality or universal determinateness — the accidentality of substance gathered into simple determinateness which however is its essential difference, specific difference. But individuality is the actual, in itself the concrete unity of genus and determinateness; here, however, in the immediate syllogism it appears at first as immediate individuality, accidentally gathered into the form of a subsistence on its own. The relation of this extreme to the middle term constitutes a categorical judgment; but since the other extreme, too, according to the above-stated determination, expresses the specific difference of the genus or its determinate principle, this other premise is also categorical.
2. This syllogism, as the first and therefore immediate syllogism of necessity, comes in the first instance under the schema of the first formal syllogism I-P-U. But as the middle term is the essential nature of the individual and not just any of its determinatenesses or properties, and as, similarly, the extreme of universality is not just any abstract universal nor again merely a single quality, but the universal determinateness, the specific principle of difference, the subject is no longer contingently united through the syllogism with any quality through any middle term. Consequently, as the relations too of the extremes to the middle term have not that external immediacy which they had in the syllogism of existence, the demand for proof, which occurred in the latter and led to the infinite progress, does not arise.
Further, this syllogism does not, as does a syllogism of reflection, presuppose its conclusion for its premises. The terms, in keeping with their substantial content, stand in a relation to one another which is in and for itself identical; we have here one essential nature pervading the three terms, a nature in which the determinations of individuality, particularity and universality are merely formal moments.
To this extent therefore the categorical syllogism is no longer subjective; in the above identity, objectivity begins; the middle term is the pregnant identity of its extremes which are contained therein in their self-subsistence, for their self-subsistence is the above substantial universality, the genus. The subjective element of the syllogism consists in the indifferent subsistence of the extremes relatively to the Notion or middle term.
3. But this syllogism still continues to be subjective, in that the said identity is still the substantial identity or content, but is still not at the same time identity of form. Consequently, the identity of the Notion is still an inner bond of union, and therefore as relation is still necessity; the universality of the middle term is substantial, positive identity, but is not equally the negativity of its extremes.
More precisely, the immediacy of this syllogism, which immediacy is not yet posited as that which it is in itself, is present in the following manner. What is really immediate in the syllogism is the individual. This is subsumed under its genus as middle term; but under the same genus come also an indefinite number of other individuals; it is therefore contingent that only this individual is posited as subsumed under it. But further, this contingency does not merely belong to the external reflection which finds the individual posited in the syllogism to be contingent by comparison with others; on the contrary, it is because the individual itself is related to the middle term as to its objective universality that it is posited as contingent, as a subjective actuality. On the other hand, in that the subject is an immediate individual, it contains determinations which are not contained in the middle term as the universal nature; therefore it also has a specific nature of its own indifferent to the middle term and possessing a content peculiar to itself. Hence, conversely, this other term also has an indifferent immediacy and an Existence distinct from the former. The same relationship also obtains between the middle term and the other extreme; for this likewise has the determination of immediacy and hence of a being that is contingent relatively to its middle term.
Accordingly, what is posited in the categorical syllogism is on the one hand extremes standing in such a relationship to the middle term that they possess in themselves objective universality or a self-subsistent nature, and at the same time appear as immediate terms and therefore as mutually indifferent actualities. But on the other hand they are equally determined as contingent, that is to say, their immediacy is sublated in their identity. But by reason of the said self-subsistence and totality of the actuality, this identity is only formal and inner; the syllogism of necessity has hereby determined itself to the hypothetical syllogism.
1. The hypothetical judgment contains only the necessary relation without the immediacy of the related terms. 'If A is, then B is'; or, the being of A is equally the being of another, of B; so far, it is not stated either that A is, or that B is. The hypothetical syllogism adds this immediacy of being:
If A is, then B is,
But A is,
Therefore B is.
The minor premise by itself enunciates the immediate being of A.
But it is not only this that is added to the judgment. The syllogism contains the relation of subject and predicate, not as the abstract copula, but as the pregnant mediating unity. Accordingly, the being of A is to be taken not as a mere immediacy, but essentially as the middle term of the syllogism. This is to be examined more closely.
2. In the first place, the relation of the hypothetical judgment is necessity or inner substantial identity associated with external diversity of Existence, or mutual indifference of being in the sphere of Appearance — an identical content which forms the internal basis. The two sides of the judgment therefore do not appear as an immediate being but as a being held within the necessity and thus at the same time as sublated being or being only in the sphere of Appearance. Further, as sides of the judgment they stand to one another as universality and individuality; one of them, therefore, is the above content as totality Of conditions, the other as actuality. It is, however, indifferent which side is taken as universality and which as individuality. That is to say, in so far as the conditions are still the inner, abstract side of an actuality, they are the universal, and it is through their being gathered together into an individuality that they enter into actuality. Conversely, the conditions are a separated, scattered Appearance which only in actuality obtains unity and significance and a universally valid existence.
The precise relation between the two sides that has here been assumed as the relation of condition and conditioned, may however also be taken as that of cause and effect, of ground and consequent — here this is indifferent; but the relation of condition corresponds more closely to the relation that obtains in the hypothetical judgment and syllogism, inasmuch as condition appears essentially as an indifferent Existence, whereas ground and cause are spontaneously transitive [ubergehend]; also condition is a more universal determination in that it comprehends both sides of the above relations, since effect, consequent, etc., is just as much condition of the cause, ground, etc., as the latter are of the former.
is the mediating being in so far as first it is an immediate being, an indifferent actuality, and secondly, in so far as it is no less an intrinsically contingent, self-sublating being. What translates the conditions into the actuality of the new shape whose conditions they are is the fact that they are not being in its abstract immediacy, but being in its Notion, in the first instance, becoming; but as the Notion is no longer transition they are more specifically individuality as self-related negative unity. The conditions are a scattered material that waits and demands to be used; this negativity is the mediating element, the free unity of the Notion. It determines itself as activity, since this middle term is the contradiction of the objective universality or the totality of the identical content, and the indifferent immediacy. This middle term is therefore no longer merely an inner necessity, but a necessity that is; the objective universality contains self-relation as a simple immediacy, as being; in the categorical syllogism this moment is in the first instance a determination of the extremes, but as against the objective universality of the middle term it determines itself as contingency, consequently, as something only posited and also sublated, that is, as something withdrawn into the Notion or into the middle term as unity, which middle term itself in its objectivity is now also being.
The conclusion, 'therefore B is', expresses the same contradiction, that B is in the form of immediate being, but equally has its being through an other, or is mediated. In respect of its form, therefore, it is the same Notion that the middle term is, distinguished from necessity only as the necessary — in the wholly superficial form of individuality as against universality. The absolute content of A and B is the same; they are only two different names for the same underlying fact for ordinary thinking [Vorstellung] which clings to the appearance of the diversified shape of determinate being and distinguishes between the necessary and its necessity; but in so far as this necessity were to be separated from B, B would not be the necessary. Thus we have here the identity of the mediating and the mediated.
3. The hypothetical syllogism in the first instance exhibits necessary relation as connection through the form or negative unity, just as the categorical syllogism exhibits through the positive unity, substantial content, objective universality. But necessity collapses into the necessary; the form-activity of translating the conditioning into the conditioned actuality is in itself the unity in which the determinatenesses of the opposition, that previously were liberated into an indifferent determinate existence, are sublated, and the difference of A and B is an empty name. Thus it is a unity reflected into itself — hence an identical content; and it is so not merely implicitly but it is also posited as such through this syllogism, in that the being of A is also not its own but B's, and vice versa, and in general the being of one is the being of the other, and in the conclusion the immediate being or indifferent determinateness appears specifically as mediated; the externality of the determinatenesses has therefore sublated itself and their unity into which they have withdrawn is posited.
The mediation of the syllogism has hereby determined itself as individuality, immediacy, and as self-related negativity, or as an identity that differentiates itself and gathers itself into itself out of that difference — as absolute form, and for that very reason as objective universality, a content that is identical with itself. The syllogism in this determination is the disjunctive syllogism.
As the hypothetical syllogism in general comes under the schema of the second figure of the formal syllogism, U-I-P, so the disjunctive syllogism comes under the schema of the third figure, I-U-P. But the middle term is the universality that is pregnant with form; it has determined itself as totality, as developed objective universality. Consequently the middle term is not only universality but also particularity and individuality. As universality it is first the substantial identity of the genus; but secondly an identity that embraces within itself particularity, but a particularity co-extensive with this identity of the genus; it is therefore the universal sphere that contains its total particularisation — the genus disjoined into its species: A that is B and C and D.
But particularisation is differentiation and as such is just as much the either-or of B, C and D, the negative unity, the reciprocal exclusion of the terms. Further, this exclusion is not merely a reciprocal exclusion, or the determination merely a relative one, but it is just as essentially a self-related determination, the particular as individuality to the exclusion of the others.
A is either B or C or D,
But A is B,
Therefore A is neither C nor D.
or again:
A is either B or C or D,
But A is neither C nor D,
Therefore A is B.
is subject not only in the two premises but also in the conclusion. In the first premise it is a universal, and in its predicate, the universal sphere particularised into the totality of its species; in the second premise it appears as determinate or as a species; in the conclusion it is posited as the exclusive, individual determinateness. Or again, it already appears in the minor premise as exclusive individuality and is positively posited in the conclusion as the determinate which it is.
Hence what appears in general as mediated is the universality of A with individuality. But the mediating factor is this A, which is the universal sphere of its particularisations and is determined as an individual. Consequently the truth of the hypothetical syllogism, namely the unity of the mediating and the mediated, is posited in the disjunctive syllogism, which for this reason is equally no longer a syllogism at all. For the middle term, which is posited in it as the totality of the Notion, contains itself the two extremes in their complete determinateness. The extremes, in distinction from this middle term, appear only as a positedness which no longer possesses any determinateness peculiar to itself as against the middle term.
Considering this point further with more particular reference to the hypothetical syllogism, we see that in the latter we had a substantial identity as the inner bond of necessity, and a negative unity distinguished therefrom — namely, the activity or form which translated one existence into another. The disjunctive syllogism is in general in the determination of universality; its middle term is the A as genus and as perfectly determinate; through this unity, that content which previously was inner is also posited and, conversely, the positedness or form is not the external, negative unity over against an indifferent existence, but is identical with the said substantial content. The whole form determination of the Notion is posited in its determinate difference and at the same time in the simple identity of the Notion.
In this way then the formalism of the syllogistic process, and with it the subjectivity of the syllogism and of the Notion in general, has sublated itself. This formal or subjective side consisted in the fact that the mediating factor of the extremes is the Notion as an abstract determination, and this latter is distinct from the extremes whose unity it is. In the consummation of the syllogism, on the other hand, where objective universality is no less posited as totality of the form determinations, the distinction of mediating and mediated has disappeared. That which is mediated is itself an essential moment of what mediates it, and each moment appears as the totality of what is mediated.
The figures of the syllogism exhibit each determinateness of the Notion individually as the middle term, which at the same time is the Notion as an ought-to-be, a demand that the mediating factor shall be the Notion's totality. But the different genera of the syllogism exhibit the stages of impregnation or concretion of the middle term. In the formal syllogism the middle term is only posited as totality by all the determinatenesses, though each singly, functioning as the mediating factor. In the syllogisms of reflection the middle term appears as the unity that gathers together externally the determinations of the extremes. In the syllogism of necessity it has likewise determined itself to the unity that is no less developed and total than simple, and the form of the syllogism which consisted in the difference of the middle term from its extremes has thereby sublated itself.
Thus the Notion as such has been realised; more exactly, it has obtained a reality that is objectivity. The first reality was that the Notion, as within itself negative unity, sunders itself, and as judgment posits its determinations in a determinate and indifferent difference, and in the syllogism sets itself in opposition to them. In this way it is still the inwardness of this its externality, but the outcome of the course of the syllogisms is that this externality is equated with the inner unity; the various determinations return into this unity through the mediation in which at first they are united only in a third term, and thus the externality exhibits in its own self the Notion, which therefore is no longer distinguished from it as an inner unity.
However, this determination of the Notion which has been considered as reality, is, conversely, equally a positedness. For it is not only in this result that the truth of the Notion has exhibited itself as the identity of its inwardness and externality; already in the judgment the moments of the Notion remain, even in their mutual indifference, determinations that have their significance only in their relation. The syllogism is mediation, the complete Notion in its positedness. Its movement is the sublating of this mediation,in which nothing is in and for itself, but each term is only by means of an other. The result is therefore an immediacy which has issued from the sublating of the mediation, a being which is no less identical with the mediation, and which is the Notion that has restored itself out of, and in, its otherness. This being is therefore a fact that is in and for itself objectivity.